Abstract

We review seven methods for adult height prediction (AHP) based on bone age, ranging from the Bayley–Pinneau method, published in 1952, to the BoneXpert method, published in 2009. These models are based on four different methods for bone age assessment including Greulich–Pyle, Tanner–Whitehouse, Fels, and the automated BoneXpert method. The aim of this chapter is to convey an understanding of the various parameters which contribute to AHP and how to best incorporate them into the AHP methods. The starting point is the Bayley–Pinneau method which predicts the fraction of adult height achieved from the bone age. Children with advanced bone age (early maturers) tend to have a stronger growth spurt, and late maturers have a weaker growth spurt. Accordingly, Bayley and Pinneau provided special AHP tables for early, average, and late maturers. The other five AHP methods reviewed are the three variants of the Tanner–Whitehouse method, TW Mark I (1975), TW Mark II (1983), and TW3 (2001), and the RWT methods of 1975 and 1993. They all model the expected adult height of children at each age using a linear model of height and bone age, and for the RWT models, also by using terms with midparental height and body weight. The main shortcoming of these models is that the linear bone age dependence is unable to describe children with constitutional delay of growth and puberty or precocious puberty. The recently developed automated BoneXpert method improves the Bayley–Pinneau method by modelling the growth potential (the fraction of adult height left to grow) as a non-linear function of two variables, bone age and bone age delay. The BoneXpert AHP method was based on the original images from the First Zürich Longitudinal Study and was subsequently validated on the more recent Third Zürich Longitudinal Study of 198 Swiss children. An additional validation study on 164 Danish children is also presented. The main advantage of the BoneXpert method is that it is based on an automated bone age which removes rater variability.

Notes

Acknowledgements

We thank Elisabeth Kaelin and Luciano Molinari for data management and Julia Neuhof for scanning of X-rays in Zürich. The Zurich Longitudinal Studies are supported by a research grant of the Swiss National Science Foundation (Grant 32473B_129956 to O.G.J.).

We acknowledge Novo Nordisk for providing the scanner used to digitize the Zürich and Björk studies.

Appendix: A Manual AHP with the BX Model

This appendix demonstrates how to perform the calculation of Fig. 3.16 manually using information in this chapter.

We consider a 13.1-year-old girl with BA 12.2 years. According to Fig. 3.2, she has a gp = 5.9%. With a current height of 167 cm, this yields a raw adult height prediction:

The population mean Hpop is assumed to be 168 cm, which is incorporated with a weight 9% from Fig. 3.6. The difference between Hraw and Hpop is 11.4 cm and 9% of this is 1.0 cm. So the final result, with the SD read from Fig. 3.9, is

$${H_{{\textrm{pred}}}} = 176.4 \pm 2.7\;{\textrm{cm}}$$

The parent’s heights are 165 and 189 cm, so the mid-parental height is 177 cm. The secular trend is assumed to be 1 cm, and the height prediction from the parents is made according to the formula in Section 3.3:

According to Fig. 3.6, this is combined with Hraw with a weight 22%, i.e. Hraw is corrected by 22% of 8.1 cm = 1.8 cm (the SD read from Fig. 3.9):

$${H_{{\textrm{predP}}}} = 175.6 \pm 2.6\;{\textrm{cm}}$$

The girl has passed her menarche, and the height at menarche was 165 cm, from which an independent AHP of 165 + 6.6 cm = 171.6 ± 2.2 cm is derived. This is combined with Hpred using a weighted average, where the weights are given by the precisions of each estimate, 0.21 and 0.14 cm–2 respectively, so 60% of the weight is from the menarche information. The best prediction becomes

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